A positive tensor network approach to simulating open quantum systems

D. Jaschke, P. Silvi, T. Calarco, A. Werner, S. Montangero, J. Eisert

Open quantum systems play an important role in quantum optics and condensed-matter physics, in 
order to study phenomena like transport properties, the interplay between Hamiltonian and 
decoherent dynamics, as well as the formation of topological order induced by dissipation. In this 
context we introduce a versatile numerically tool that allows for the simulation of one-dimensional 
open quantum systems while ensuring positivity of the operators in every step of the algorithm. At 
the heart of the construction are matrix product density operators (MPDO) capturing purifications 
of mixed states, for which we suggest a stable and efficient scheme of manipulation preserving the 
form of the tensors and keeping both bond and Kraus dimensions fixed. To exemplify the functioning 
of the approach, we study both stationary states and transient dissipative behaviour, for systems 
of coupled cavities and transport problems in dissipative quantum many-body systems.